Pade-type higher-order boundary filters for the Navier-Stokes equations

Abstract

The use of procedures based on higher-order finite-difference formulas is extended to solve complex fluid-dynamic problems on highly curvilinear discretizations and with multidomain approaches. The accuracy limitations of previous near-boundary compact filter treatments are overcome by derivation of a superior higher-order approach. For solving the Navier-Stokes equations, this boundary component is coupled to interior difference and filter schemes with emphasis on Pade-type operators. The high-order difference and filter formulas are also combined with finite-sized overlaps to yield stable and accurate interface treatments for use with domain-decomposition strategies. Numerous steady and unsteady, viscous and inviscid flow computations on curvilinear meshes with explicit and implicit time-integration methods demonstrate the versatility of the new boundary schemes.